Dispersion-Accounting DFT Methods

Recently introduced double-hybrid functionals (see [30] and the references therein) recover dispersion energy, but only to a hmited extent, as nonlocal correlation terms are too small to recover the full non-covalent interaction energy [28]. They are also considerably more computationally expensive than GGA, mGGA, and even hybrid functionals. 

Therefore, some special dispersion-accounting [31] DFT methods are needed for reliable description of these interactions. These methods may initially account for dispersion in a nonempirical way (i.e., include the nonlocal term in that accounts for dispersion) or may incorporate empirical dispersion corrections (in a force-field manner). Our emphasis is on these two methods, which are commonly used in modeling of transition metal-containing graphene systems. Other methods designed to account for dispersion interactions are also available but are beyond the scope of our discussion. The reviews on dispersion-accounting DFT methods are available elsewhere [24, 28]. 

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S22, S66, and S66 x 8 were developed and represent a number of Ej, values of organic molecule dimers calculated with state-of-the-art electron correlation methods [2]. Approximate (importantly, dispersion-accounting DFT methods) computational methods are often tested against these databases and quite often initially parameterized to reproduce these data. Therefore, these datasets represent benchmarks that help to validate a recently introduced method or to parameterize a new one. 

Crystal structure prediction The field of organic crystal structure prediction remains one of the best testing grounds for intermolecular potentials. Acciuades need not be as high as that needed for spectroscopic calculations, but the effects of molecular flexibility and many-body non-additivity need to be accounted for. See Price (2008, 2009) for recent reviews of this subject. For a description of dispersion-corrected DFT methods specially parametrized for organic crystals see Neumann and Perrin (2005). For a comprehensive examination of the role of detailed distributed multipole models in this field see Day et al. (2005). 

To give an overview of the subject, quantum chemical methods that properly account for dispersion are discussed in more details in this chapter. These, however, are limited to several wave function theory and two dispersion-accounting density functional theory (DFT) methods. In fact, many dispersion-accounting DFT approaches have been developed recently but only few of them are widely used in modeling of transition metal-graphene systems. 

Despite all the advantages of the DFT method one should be aware of well known failure of this method. Exchange-correlation functionals currently available are not capable to account for dispersion interaction, e. g., interaction between zeolite channel wall and hydrocarbons cannot be properly described at the DFT level (sec section 4.3). 

In particular, electron correlation effects are crucial to describe the vdW interaction. To account for the electron correlation effects, density functional theory (DFT) is widely used. As the former interaction is mainly caused by electrostatic interaction between the base pairs, it is sufficient to describe it with the hybrid DFT methods. On the other hand, it is rather difficult to describe the latter interaction by means of the standard hybrid DFT because of the lack of the weak dispersion force. The latter interaction is so weak that the post Hartree-Fock (HF) theories such as the second order of Mpller-Presset perturbation theory (MP2) and coupled-cluster method (CC) are at least required to describe it qualitatively. In 2004, Hobza et al. estimated accurate interaction energies between stacked bases by using MP2 based on the resolution of identity method (RI-MP2), with complete basis set (CBS) corrections [1,2]. 

However, care has to be taken when applying DFT to hydrocarbon species in zeolites. The currently available functionals do not properly account for dispersion, which is a major stabilizing contribution for hydrocarbon-zeolite interactions. Due to the size of the systems it is difficult to apply wavefunction-based methods such as CCSDfT) or MP2. Thanks to an effective MP2/DFT hybrid approach and an extrapolation scheme energies, including the dispersion contribution, are now available for the different hydrocarbon species of Fig. 22.1 [50]. 

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